Bernard Frénicle de Bessy (c. 1604 – 1674), was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics. He is best remembered for , a treatise on magic squares published posthumously in 1693, in which he described all 880 essentially different normal magic squares of order 4. The Frénicle standard form, a standard representation of magic squares, is named after him. He solved many problems created by Fermat and also discovered the cube property of the number 1729 (Ramanujan number), later referred to as a taxicab number. He is also remembered for his treatise Traité des triangles rectangles en nombres published (posthumously) in 1676 and reprinted in 1729.
Bessy was a member of many of the scientific circles of his day, including the French Academy of Sciences, and corresponded with many prominent mathematicians, such as Mersenne and Pascal. Bessy was also particularly close to Fermat, Descartes and Wallis, and was best known for his insights into number theory.
thumb|Frenicle's Methode, 1754 edition.
In 1661 he proposed to John Wallis a problem of what amounted to the following system of equations in integers,
:x<sup>2</sup> + y<sup>2</sup> = z<sup>2</sup>, x<sup>2</sup> = u<sup>2</sup> + v<sup>2</sup>, x − y = u − v > 0.
A solution was given by Théophile Pépin in 1880.
La Méthode des exclusions
Frénicle's La Méthode des exclusions was published (posthumously) in 1693, which appeared in the fifth volume of (1729, Paris), though the work appears to have been written around 1640. The book contains a short introduction followed by ten rules, intended to serve as a "method" or general rules one should apply in order to solve mathematical problems.